Population and Percentage

Date: 03/07/99 at 23:12:30
From: Ian Hubble and Ross Hubble
Subject: Population and Percentage

Between 1902 and 1952, the population of Maranga increased by 30,000.  
Dividing the population up into adults and children, and males and 
females, the following information can be given about the number of 
men, women, boys, and girls.

In 1902, the census showed that 60% of the people were males. There 
were half as many boys as females, and for every four boys there were 
three girls.

At the time of the 1952 census, 25% of the total were children. The 
number of adults was five times the number of boys, and there were as 
many women as there were males. The number of children equalled the 
number of females in 1902.

How many women were there in 1902, and how many in 1952?

We have worked through this and by logic and algebra have found

            1902        1952
men          40%         30%
women        25%         45%
boys         20%         15%
girls        15%         10%

What we are stuck on is linking the 30,000 increase and % change to 
work out the number of women.  

Can you please help?

Date: 03/08/99 at 05:37:58
From: Doctor Allan
Subject: Re: Population and Percentage

If we call the population number in 1902 X and the population number in 
1952 Y, we have two useful pieces of information. We know that the 
number of children in 1952 equals the number of females in 1902. Since 
the number of females equals 40% of the total population in 1902 and 
the number of children equals 25% of the population in 1952, we have:

(1)  0.40*X = 0.25*Y

Furthermore, we know that the population increase is 30,000. This means 
that 

(2)  Y - X = 30000

We now have two equations with two unknowns, which we can solve the 
usual way. Isolate Y in (2) to get
 
(2')  Y = 30000 + X 

and substitute this into (1) yielding

(1')  0.40*X = 0.25*(30000 + X)
      0.40*X = 7500 + 0.25*X
      0.15*X = 7500
           X = 50000

Substituting this value into (2') yields

(2'')  Y = 80000

We have figured out the total population of 1902 and 1952. Now the 
number of women can be easily calculated by using their percentage-rate 
of the total population.

- Doctor Allan, The Math Forum
  http://mathforum.org/dr.math/